On the coupling between membrane bending and stretching in lipid vesicles
The formation of a lipid vesicle from a lamellar phase involves a cost in bending energy of 100-1000 times the thermal energy for values of the membrane bending rigidity{kappa} typical for phospholipid bilayers. The bending rigidity of a bilayer is however a strongly decreasing function of its thickness h, and the bilayer can thus reduce its bending energy by stretching (and thus thinning) the bilayer. In this paper, we construct a simple model to describe this mechanism for the coupling between bending and stretching and analyse its effect on the bending energy and thermal fluctuations of spherical lipid vesicles. We show that the bilayer thinning becomes significant for small vesicles, and for a vesicle with radius R0 [~] 15 nm there is a sizeable thinning of the bilayer compared to the planar state. We furthermore demonstrate how this thinning is associated with a significant decrease in free energy due to the thermally excited bending modes. We argue that this previously unexplored effect can explain the experimentally observed lower limit of achievable vesicle sizes, which eventually become unstable due to the thinning of the bilayer. We also sketch how this effect provides a potential generic mechanism for the strong curvature dependence of protein adsorption to lipid membranes.